Continuity mistake: After beating the lake monster Del Lago and going through the cutscene and chapter end, you can take the boat out on the lake. When you come up to a dock, you can bring the boat up to either side. The cutscene always shows Leon pulling the boat up to the same side of the dock, regardless of which side you chose beforehand.
Other mistake: After fighting the lake monster, if Leon is wearing his police uniform (unlocked after beating the game), in the next cutscene he has a nightmare about the Las Plagas in his body. He looks down at his arm (which is now infected with the Las Plagas) and screams, but since the jacket is covering his arm, he would not have been able to see it.
Continuity mistake: During the first knife fight with Krauser shortly before fighting "it" Leon's knife changes hands several times, one particularly notable part is just before he cuts Krauser across the chest, Leon drops his knife with his left hand and grabs it with his right, but in the previous shot, he was holding the knife in his right hand anyway.
Continuity mistake: When you fight the first El Gigante the gates open so you can head to the church. Before you go through the doors look up at the sky, you notice its just a plain night sky. When you exit (walkway to the church) it's pouring down rain. Even before the boss fight it's raining, so why is it not raining only in this area?
Continuity mistake: Shortly after Leon's first encounter with Bittorez Mendez (where Mendez chokes Leon, then walks through a door that Leon just passed through), Leon can trigger a cut scene in which he is attacked a second time by trying to follow Mendez, Ada will shoot Mendez, putting several bullet holes in his coat to get Mendez to leave Leon alone. However, when Leon fights Mendez in the barn, the bullet holes in his coat are visible in the cut scene whether the previous cut scene, forcing Ada to fire at him, was activated or not.